A369511 Expansion of (1/x) * Series_Reversion( x * ((1-x)^2-x^3)^2 ).

1, 4, 26, 206, 1815, 17082, 168159, 1710234, 17828973, 189504744, 2045971440, 22374997320, 247344411792, 2759394009008, 31027178033064, 351270123392892, 4000793799046578, 45809545263096832, 527010005799822844, 6088666065809281348, 70612995488695876634

Offset: 0

Author

Seiichi Manyama, Jan 25 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A368962, A369514.

Cf. A369214.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^2-x^3)^2)/x)

PARI

a(n) = sum(k=0, n\3, binomial(2*n+k+1, k)*binomial(5*n-k+3, n-3*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+k+1,k) * binomial(5*n-k+3,n-3*k).